Welcome to the website of researchers working in Bilbao (either at UPV/EHU or at BCAM) in mathematical analysis, partial differential equations, inverse problems, mathematical physics, and/or related topics.
UPV/EHU, Thursday, September 11th, 2025, 12:00 - 13:00
Title: Large deviations in the semi-classical limit of quantum spin systems
Christiaan J.F. van de Ven - Friedrich-Alexander University Erlangen-Nürnberg
The continuous $C^*$-bundle generated by Berezin-Toeplitz quantization on a symplectic manifold provides a rigorous framework for describing the semiclassical limit of quantum systems. The rate of convergence in this limit, often quantified by a rate function or entropy, is naturally formalized through the theory of large deviations. In this work, I investigate the specific case of the complex projective line, which serves as the phase space for a single quantum spin system. The spin, which characterizes the system's quantum nature, defines the semiclassical parameter and corresponds to the dimension of the associated Hilbert space. More precisely, we establish a full large deviation principle for the local Gibbs state and explicitly characterize the corresponding rate function. This is done by using a sophisticated argument based on the Feynman-Kac integral.